Stereotype is a dirty word in our society because no one wants to be generalized. Yet most people throw the word around without really knowing it in a literary context, as the use of commonly-known generalizations to build two-dimensional, rubber-stamped characters.
Generalizations don't always destroy a story. Archetype is the good use of a generalization to build deep characters on a familiar foundation. What's the difference? Archetype helps frame a story, while stereotype only serves as a substitute for complex people: the "hero on a quest" is an archetype, while "the drunken Irishman" is a stereotype. Maybe you could create a good story about a drunk Irish hero on a quest--but he MUST have deep individual traits that make him unique. A writer over at Enchanted Inkpot says best: archetype means using generalization as a beginning from which to work a story, while stereotype uses generalization as its end.
You can think about stereotypes in three classes: stereotypical characters, behaviors, and situations. Writers often already know to avoid stereotyping characters with features such as race, socioeconomic status, or sexual orientation. However, the other two types of stereotypes should be avoided with as much diligence.
Perhaps the hardest stereotypes to avoid are behavior stereotypes, especially those centered on beliefs. Intolerant Christian parents, licentious atheists, rugged individualists, ever-meditating Buddhists, and radical communists are very prevalent behavioral stereotypes. Behavior stereotypes dominate film industry and pop culture. Think about the frequency with which you’ve been exposed to a hostile minority, or a mother begging her daughter to find a husband and settle down. These are behavioral stereotypes that show little imagination.
You should also think about avoiding situational stereotypes like the faithful dog rescuing Jimmy out of the well, or the classic boy and girl meet and hate each other but end up falling in love. Situational stereotypes may not be perpetuating a negative social idea in the way of character and behavioral stereotypes, but threaten to bore readers.
Avoiding all three classes of stereotype is a great start to ensuring your story will bring innovation to print, and lack unwanted predictability. Good characters--even villains--are people like you, not just cardboard cut-outs for you to thumb-tack your plot and themes onto at will. Likewise, well thought out behaviors and scenarios should keep the reader engaged and guessing at every turn.